1. In a Pint glass, add rye whiskey, peychauds bitters, sugar cube and stir gently to break up the sugar.
2. Scoop in the ice cubes and mix, gently stir until sugar is dissolved.
3. In a cocktail glass, add the Absinthe and swirl the glass around to coat its inner walls with it. Decant the extra Absinthe off.
4. Using a julep strainer, strain the contents of the Pint glass into the cocktail glass.
5. Garnish with a lemon twist and serve chilled.